The coherent emission from nuclei arranged in a crystal lattice gives rise to \(\gamma \) -ray emission along directions determined by the condition of constructive far-field interference, similar to the Smith-Purcell effect for grating structures [1]}, [2]}. We consider a homogeneous crystalline film consisting of \(N\)  atomic planes with one emitting nucleus in each two-dimensional (2D) unit cell of each of those planes. For simplicity, we take the film to be normal to the \(z\)  axis (i.e., we consider normally impinging beams). The crystal structure can then be defined in terms of the 2D reciprocal lattice and the three-dimensional displacement vector \({\bf b}={\bf b}_\parallel +b_z\hat{\bf z}\)  separating the reference nuclei in two consecutive atomic planes.
